A new proof of a theorem of Littlewood

Abstract In this paper we give a new combinatorial proof of a result of Littlewood [3]: , where Sµ denotes the Schur function of the partition µ, n(µ) is the sum of the legs of the cells of µ and h (µ) (s) is the hook number of the cell s ∈ µ

The weighted hook length formula

Based on the ideas in [CKP], we introduce the weighted analogue of the branching rule for the classical hook length formula, and give two proofs of this result. The first proof is completely bijective, and in a special case gives a new short combinatorial proof of the hook length formula. Our second proof is probabilistic, generalizing the (usual) hook walk proof of Green-Nijenhuis-Wilf, as well as the q-walk of Kerov. Further applications are also presented.Comment: 14 pages, 4 figure

A new proof of a theorem of Littlewood

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